SOLUTION: Graph the relation: |x|/5+|y|/3=1 and find the area enclosed by the graph. Hint: Solve for all possible expressions in terms of y before you graph. A. 20 B. 30 C. 40

Algebra ->  Surface-area -> SOLUTION: Graph the relation: |x|/5+|y|/3=1 and find the area enclosed by the graph. Hint: Solve for all possible expressions in terms of y before you graph. A. 20 B. 30 C. 40       Log On


   

Question 1172848: Graph the relation: |x|/5+|y|/3=1 and find the area enclosed by the graph.
Hint: Solve for all possible expressions in terms of y before you graph.
A. 20 B. 30 C. 40 D. 50
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

system%28x%2F5%2By%2F3=1%2Cx%2F5-y%2F3=1%2C-x%2F5%2By%2F3=1%2C-x%2F5-y%2F3=1%29

Those four expressions are taken in quadrants QI, QII, QIII, and QIV respectively. 

The graph is this rhombus:



Its area consists of four right triangle each with base 5 and height 3.

Each triangle has area A=expr%281%2F2%29%2Ab%2Ah=expr%281%2F2%29%285%29%283%29=15%2F2.

Since there are 4 congruent right triangles in the area of the rhombus,

the answer is 4%2A%2815%2F2%29=30, choice B.

Edwin